44. Starting from rest, a 64.0-kg person bungee jumps from QIC a tethered hot-air balloon 65.0 m above the ground. The bungee cord has negligible mass and unstretched length 25.8 m. One end is tied to the basket of the balloon and the other end to a harness around the person's body. The cord is modeled as a spring that obeys Hooke's law with a spring constant of 81.0 N/m, and the person's body is modeled as a particle. The hot-air balloon does not move. (a) Express the gravitational potential energy of the person-Earth sys- tem as a function of the person's variable height y above the ground. (b) Express the elastic potential energy of the cord as a function of y. (c) Express the total potential energy of the person-cord-Earth system as a function of y. (d) Plot a graph of the gravitational, elastic, and total potential ener- gies as functions of y. (e) Assume air resistance is negligible. Determine the minimum height of the person above the ground during his plunge. (f) Does the potential energy graph show any equilibrium position or positions? If so, at what elevations? Are they stable or unstable? (g) Determine the jumper's maximum speed.

1. A 5.00-kg block is set into motion up an inclined plane with an initial speed of v; = 8.00 m/s. The block comes to rest after traveling 3.00 m along the plane, which is inclined at an angle of 30.0° to the horizontal. For this motion determine (a) the change in the block's kinetic energy, (b) the change in the potential energy of the block- Earth system, and (c) the friction force exerted on the block (assumed to be constant). (d) What is the coefficient of kinetic friction?

A 69.0-kg athlete leaps straight up into the air from a trampoline with an initial speed of 8.9 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height. Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer.

Can the work done by Friction be zero? In a case where static friction exists, the object does not move and the change in kinetic energy is also zero? W = Fd = ?KE = 0? What did I do wrong?

A 5.80-kg block is set into motion up an inclined plane with an initial speed of v₁ = 8.20 m/s (see figure below). The block comes to rest after traveling d = 3.00 m along the plane, which is inclined at an angle of 0 = to the horizontal. V. (a) For this motion, determine the change in the block's kinetic energy. (b) For this motion, determine the change in potential energy of the block-Earth system. (c) Determine the friction force exerted on the block (assumed to be constant). N (d) What is the coefficient of kinetic friction?

A 7.80 g bullet is moving at 460 m/s just before it penetrates a tree trunk to a depth of 4.9 cm (ay What the magnitude of the average frletional force (In N) that is exerted on the bullet whille moving the tree trunk? Uso work considerations to o your answer. (b) Asturing the frictional force is constant, how much time elapses between the moment the bullet enters the tree trunk and the moment it moving?

If the net work done by the force is 4 Joules, what is the value for z in the attached graph?

Based on your measurements of vertical position vs time you should have noticed that the maximum height of the ball decreases with each subsequent bounce. A basic analysis of kinetic energy and gravitational potential energy conservation would imply that each bounce should result in the ball returning to the same height from which it was initially dropped. Explain why the height of each subsequence bounce decreases, and why this does not violate the overall conservation of energy.

A 7.80-g bullet moving at 590 m/s penetrates a tree trunk to a depth of 5.60 cm. (a) Use work and energy considerations to find the average frictional force that stops the bullet. N=(b) Assuming the frictional force is constant, determine how much time elapses between the moment the bullet enters the tree and the moment it stops moving. s=